Generally yes. Sometimes you run into complications such as not enough space in the box to connect up the new wires coming in.
Original BX cable is not code compliant. Its spiral sheath is not a good and sufficient ground. Nowadays, most spiral wrapped cabling must have a straight grounding strip or wire running through it.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.